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Medians & Altitudes of Triangles

Medians & Altitudes of Triangles. P, R, Rh,S 11. 25,65,65,90 P, R, Rh,S 12. 4 P, R, Rh,S 13. 10 P, R, Rh,S 14. 18, 72, 72 P, R, Rh,S 15. 13.5 R, S 16. 2 Rh , S 17. 32, 58, 58 Rh , S 18. 9 R, S 19. 1/2 Rh , S 10 25. 15 30 27. 60.

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Medians & Altitudes of Triangles

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  1. Medians & Altitudes of Triangles

  2. P, R, Rh,S 11. 25,65,65,90 • P, R, Rh,S 12. 4 • P, R, Rh,S 13. 10 • P, R, Rh,S 14. 18, 72, 72 • P, R, Rh,S 15. 13.5 • R, S 16. 2 • Rh, S 17. 32, 58, 58 • Rh, S 18. 9 • R, S 19. 1/2 • Rh, S • 10 25. 15 • 30 27. 60 HW answers p. 187

  3. p. 188 # 28 B A Given: ABZY; ZY  BX; 1  2 Prove: ABZY is a rhombus 1 2 3 X Y Z Statements Reasons • ABZY; ZY  BX; 1  2 1. Given • BX  BZ 2. Isosceles Triangle Them • ZY  BZ 3. Substitution • ABZY is a rhombus 4. A parallelogram with congruent consecutive sides

  4. p. 188 # 29 B A Given: ABZY; AY  BX Prove:1  2; 1   3 1 2 3 X Y Z Statements Reasons • ABZY; AY  BX 1. Given • AY  BZ 2. Opp sides of a p-gram are  • BX  BZ 3. Substitution • 1  2 4. Isosceles Triangle Theorem • 3  2 5. // lines form  corr. Angles • 1  3 6. Substitution

  5. Trapezoids

  6. Trapezoid – a quadrilateral with exactly ONE pair of parallel sides.

  7. Properties of a Trapezoid: Base angles bases : parallel sides : non-parallel sides legs : angles formed by a base and a leg. base angles base leg leg base

  8. A Special Trapezoid… Isosceles  W X Z Y Isosceles Trapezoid: A trapezoid with legs. congruent Theorem: Base angles of an isosceles trapezoid are . congruent If trap WXYZ has WZ  XY, then W  X and Y  Z .

  9. Median of a Trapezoid – a segment in a trapezoid that connects the two midpoints of the non-parallel sides. LO is the median of the trapezoid. J K L O N M JO @ ON KL @ LM O is the ______ of JN. L is the ______ of KM. midpoint midpoint

  10. 16 + 10 2 = 13 The length of the median of a trapezoid is the average of the lengths of the parallel sides. 16 13 10

  11. 4 12 7 19 10 26 15 20 15 20 10 25

  12. 7x+3 Algebra Connection 7(4) + 3 = 31 2(4) – 1 = 7 19 2x - 1

  13. 6x + 10 Algebra Connection 6(5) + 10 = 40 8(5) + 20 = 60 x + 45 5 + 45 = 50 8x + 20

  14. Algebra Connections Practice HW p. 192 1-17, 21, 22, 23

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